The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A100284 Expansion of (1-4*x-x^2)/((1-x)*(1-4*x-5*x^2)). 4
 1, 1, 5, 21, 105, 521, 2605, 13021, 65105, 325521, 1627605, 8138021, 40690105, 203450521, 1017252605, 5086263021, 25431315105, 127156575521, 635782877605, 3178914388021, 15894571940105, 79472859700521, 397364298502605 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Binomial transform of A054881. Binomial transform of A179607. - Johannes W. Meijer, Aug 01 2010 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,1,-5) FORMULA a(n) = 5*a(n-1) + a(n-2) - 5*a(n-3). a(n) = (1/6)*(3 + 5^n + 2*(-1)^n). E.g.f.: (1/6)*(exp(5*x) + 3*exp(x) + 2*exp(-x)). - G. C. Greubel, Feb 06 2023 MATHEMATICA CoefficientList[Series[(1-4x-x^2)/((1-x)(1-4x-5x^2)), {x, 0, 30}], x] (* or *) LinearRecurrence[{5, 1, -5}, {1, 1, 5}, 30] (* Harvey P. Dale, Apr 01 2013 *) PROG (Magma) [(5^n +2*(-1)^n +3)/6: n in [0..40]]; // G. C. Greubel, Feb 06 2023 (SageMath) def A100284(n): return (1/6)*(5^n +1 +4*((n+1)%2)) [A100284(n) for n in range(41)] # G. C. Greubel, Feb 06 2023 CROSSREFS Cf. A054881, A100285, A100286, A179607. Sequence in context: A280623 A203154 A097175 * A337168 A341853 A260845 Adjacent sequences: A100281 A100282 A100283 * A100285 A100286 A100287 KEYWORD easy,nonn AUTHOR Paul Barry, Nov 11 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 28 01:34 EDT 2024. Contains 372900 sequences. (Running on oeis4.)